The former chief executive of online brokerage E*Trade Financial Corp
Donald Layton, who is one of three finalists being considered for the job, had met with Freddie's federal regulator last month, the people told the paper.
No final decision or job offer has been made, but there will be a decision in the next week, a person close to the situation told the Journal.
Freddie Mac could not immediately be reached for comment by Reuters outside regular U.S. business hours.
(Reporting by Sakthi Prasad; Editing by David Holmes)